CEVAP:

In multiple linear regression, there are observed values of k (k?2) independent variables, with n observations, like x1= x1, x12, x13, ..., x1n ; x2= x21, x22, x23, ..., x1n ; ... ; xk
= xk1, xk2 xk3 , ..., xkn. There is alsothe values of one dependent variable, y= y1, y2, y3, ..., yn. In order to show a possible linear relationship between k(k?2) independent variables and dependent variable (y), the following multiple linear regression model can be written as follows:
yi = ß0 +ß1x1i +ß2x2i +ß3x3i +...+ßkxki +?i (i =1,....,n;n ? k +1)

In this multiple linear regression model:
yi : i th observation’s value of the dependent variable,
x1i : i th observation’s value of the first independent variable,
xki : i th observation’s value of the kth independent variable,
?i : random error (the mean of it is zero),
k : the number of independent variables,
ß0, ß1, ß2, ... , ßk : the population parameters to be estimated by sample data.

If you remember the simple linear regression model, the general structure is still the same. Now in multiple linear regression, the constant of simple linear regression ? is represented by ß0. The linearity of the model comes from the parameters of the model. It is possible to include the powers of any independent variable (such as squares) into the model as a new independent variable. Here, again the model of least squares is used to estimate the values of the population parameters of multiple linear regression. But in order to use the model of least squares, we need to transform our data in to matrix form.